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§ Counting

Even & Odd Numbers

§ Counting

Even & Odd Numbers

CCSS.2.OA.33 min read

Even numbers end in 0, 2, 4, 6, or 8 and divide exactly by 2 without remainder. Odd numbers end in 1, 3, 5, 7, or 9 and always leave a remainder of 1 when divided by 2. This fundamental classification appears throughout Key Stage 1 and forms the foundation for understanding divisibility, patterns, and number properties in later mathematics.

§ 01

Why it matters

Even and odd numbers appear constantly in real-world situations. Bus routes often run every 2 minutes (even intervals), whilst football matches have 22 players (an even number ensuring equal teams). Shop prices like £3.99 use odd numbers to appear smaller. In mathematics, understanding even and odd properties helps solve problems about divisibility by 2, identify patterns in sequences, and predict outcomes in algebra. The concept supports Year 2 number work and builds toward GCSE topics like modular arithmetic and proof techniques. Programmers use even-odd tests to create alternating patterns in code, whilst statisticians rely on these classifications when analysing data sets with thousands of values.

§ 02

How to solve even & odd numbers

Even & Odd Numbers

  • Even numbers end in 0, 2, 4, 6, or 8. They divide exactly by 2.
  • Odd numbers end in 1, 3, 5, 7, or 9.
  • Even + even = even. Odd + odd = even. Even + odd = odd.
  • Even × any = even. Odd × odd = odd.

Example: 14 is even (ends in 4). 23 is odd (ends in 3).

§ 03

Worked examples

Beginner§ 01

Which of these are odd? 6, 7, 10

Answer: 7

  1. Check each number → 6=even, 7=odd, 10=even — Odd numbers have a remainder of 1 when divided by 2.
Easy§ 02

How many even numbers? 3, 22, 13, 17, 21, 18

Answer: 2

  1. Check each number and count the even ones → 2 even numbers — Even numbers in the list: 18, 22. That is 2.
Medium§ 03

List all odd numbers between 21 and 29.

Answer: 21, 23, 25, 27, 29

  1. Go through each number from 21 to 29 → Check numbers 21 to 29 — An odd number is not divisible by 2. It ends in 1, 3, 5, 7, or 9.
  2. List all odd numbers in the range → 21, 23, 25, 27, 29 — The odd numbers between 21 and 29 are: 21, 23, 25, 27, 29.
§ 04

Common mistakes

  • Confusing zero's classification: 0 is even (ends in 0), not odd, yet some classify it incorrectly as odd.
  • Misapplying addition rules: calculating 7 + 9 = 16 correctly but incorrectly stating that odd + odd = odd instead of even.
  • Looking only at the first digit: identifying 31 as odd because it starts with 3, rather than checking the units digit.
§ 05

Frequently asked questions

Is zero even or odd?
Zero is even because it ends in 0 and divides exactly by 2 (0 ÷ 2 = 0 with no remainder). Any number that divides exactly by 2 is even by definition.
What happens when you add an even and odd number?
Even + odd always equals odd. For example, 6 + 7 = 13. This happens because the even number contributes pairs whilst the odd number adds one extra.
How can you quickly identify odd numbers?
Look at the units digit (rightmost digit). If it's 1, 3, 5, 7, or 9, the entire number is odd, regardless of how many digits it has.
What's the pattern when multiplying even and odd numbers?
Even × any number = even. Odd × odd = odd. This means 8 × 15 = 120 (even), but 7 × 9 = 63 (odd). Even numbers always produce even products.
Are negative numbers even or odd?
Yes, negative numbers follow the same rules. -4 is even (ends in 4), whilst -7 is odd (ends in 7). The sign doesn't affect the even-odd classification.
§ 06

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